(Almost) Model-Free Recovery

Under mild assumptions, we recover the model-free conditional minimum variance projection of the pricing kernel on various tradeable realized moments of market returns. Recovered conditional moments predict future realizations and give insight into the cyclicality of equity premia, variance risk premia, and the highest attainable Sharpe ratios under the minimum variance probability. The pricing kernel projections are often U-shaped and give rise to optimal conditional portfolio strategies with plausible market timing properties, moderate countercyclical exposures to higher realized moments, and favorable out-of-sample Sharpe ratios.